Best for mostAnthony Briggs · 2005
Anthony Briggs's Penguin translation is the one I'd start with — modern, flowing, and the easiest way into a very long book. The one knock worth knowing: he gives some of the soldiers British colloquialisms that can feel oddly 20th-century. Minor against how readable the whole thing is, and Orlando Figes's afterword is a bonus. This is where I'd start.
Most faithfulLouise & Aylmer Maude · 1923
Louise and Aylmer Maude knew Tolstoy and translated with his blessing, and their version — revised and updated by Amy Mandelker for Oxford — is still the one many readers call the most faithful that's also pleasant to read. If you want the closest thing to an authorized War and Peace, this is it.
Most literalPevear & Volokhonsky · 2007
Pevear and Volokhonsky stay close to the Russian and keep Tolstoy's French passages in French, with translations in the notes — which is how Tolstoy wrote it. Faithful and dense; some readers find it heavier going than Briggs or Maude. The choice if you want the texture of the original over smoothness.
The free classicConstance Garnett · 1904
Constance Garnett's century-old translation is out of copyright and free. It reads smoothly, in an older English, and it's how generations first read the book. Complete and free — a fine way to begin, knowing the newer translations are more accurate.